This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.

Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an

The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is called the spectrum. We describe how the spectrum determines a Riemannian m

For a Riemannian manifold M, the geometry, topology and analysis are interrelated in ways that have become widely explored in modern mathematics. Bounds on the

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical